Question

What are the common factors of 24 and 32?

Answer 1

Hint: To find the common factors of 24 and 32, we have to list the factors of each of these numbers. Let us consider the factors of c. Suppose we get c by multiplying a and b, that is, $a\times b=c$ , then a and b are the factors of c. Similarly, we can get the factors of 24 and 32 and take the common factors in them.

Complete step by step solution:
We have to find the common factors of 24 and 32. When a number is multiplied by another number and we get the given number, then the numbers multiplied will be the factors of the given number. Let us consider the factors of c. Suppose we get c by multiplying a and b, that is, $a\times b=c$ , then a and b are the factors of c.
Let us now list the factors of each of the given numbers.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32 are 1, 2, 4, 8, 16, 32
We have to find the common factors 24 and 32. We can see that 1, 2, 4, and 8 are the common factors.

Note: Students must note that a number will have at least 2 factors, that is, 1 and the number itself. They must also note that the factors of a number will never be greater than that number. We can also find the common factors in an alternate way.
Let us first find the Greatest Common Divisor (GCD) of 24 and 32. For this we will divide the largest number by the smallest. If the remainder is 0, then the smallest number will be the GCD. If the remainder is not zero, then we will further divide the smallest number by the remainder of the first division. The GCD will be the divisor.
$\dfrac{32}{24}=1$ Remainder =8
$\dfrac{24}{8}=3$ Remainder =0
Hence, GCD of 32 and 24 are 8.
The common factors of 32 and 24 will be the factors of 8 =1, 2, 4, 8.